Nonlinear optical element

ABSTRACT

A nonlinear optical element for use in a light-light switching element or optical memory element of an optical information system which is controlled by a control light. The nonlinear optical element comprises an optical active layer having dielectric samples or semiconductor samples which cause a nonlinear optical effect, wherein their shapes and sizes are selected so that the electric field of exciton resonance energy in the sample increases in resonance with the size of the sample.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a nonlinear optical element used in the opticalelectronics field such as an optical signal processing element or anoptical memory element which can control light, and a nonlinear opticalstructural body which can be used as material of the nonlinear opticalelement and can provide a nonlinear optical effect.

2. Discussion of the Related Art

In recent years, it has been desirable to develop optically controlledoptical switching elements or optical memory elements which can controlan optical output by a control light for realizing an opticalinformation transmission apparatus or optical information processingapparatus which can process a large capacity and high speed informationtransmission and information processing.

An effect in which optical characteristics depend on the input opticalintensity is referred to as a "nonlinear" effect. In general, when theinput optical intensity is small, an optical response such as areflected light spectrum or a transmitted light spectrum does not dependon the input optical intensity. These responses are referred to aslinear responses because the amount of the induced polarization isproportional to the first order of the electric field in the medium.But, if the input optical intensity becomes large, for example, when twokinds of strong and weak lights are inputted, a phenomenon occurs inwhich a response of the weak light is varied by the strong light and aresponse of the strong light is varied by its own intensity. Byutilizing such phenomena, an optical response such as a reflection or atransmission is controlled by its own light or other input lights.

At present, them are several types of nonlinear optical elements ornonlinear optical structural bodies studied for light-light controlsystems in which the light is controlled by the light. They are, forexample, elements using the nonlinear optical effect occurred by theband filling effect using transition between bands in the GaAs quantumwell and so on, elements using nonlinear motion of the free carriers inthe semiconductor having narrow band gap such as InSb, or excitonicresonance type of optical material using a resonance of the excitonlevel in the bulk semiconductor, or exciton levels confined in thesemiconductor quantum wells and microcrystallites. Optical switchingelements and optical bi-stable elements also use the above elements.

As described above, optical switches driven by light-light control oroptical memories are needed for an optical information processing systemwhich processes a large capacity of information at high speed. In theseelements, an interaction amount between lights becomes a big problem forcontrolling or processing light signals using the light. The lighthaving no interaction in the vacuum gives an interaction between lightsvia polarization of its medium. The amount of interaction is decided byan amount of the intrinsic nonlinear polarization of the medium anddepends on the intensity of the light.

FIG. 14 is a conceptual figure showing an operation of a conventionalnonlinear optical element. In the FIG. 10 is an optical medium whichcauses a nonlinear optical effect. 4 is input light provided into theoptical medium 10. 5 is control light inputted into the optical medium10. 6 is output light including input light 4 passed through the opticalmedium 10. The intensity of the output light 6 is obtained by modulatingthe input light 4 and varying intensity of the control light 5 under thenonlinear optical effect of the optical medium 10. The reflection lightis also modulated in the same way, but not shown in FIG. 14.

Generally, light-light interaction is very small in natural material. Inorder to carry out light-light control in the optical informationprocessing, it is necessary to have very strong intensity of the controllight. There has been no suitable example of a nonlinear optical elementso far which can provide the light-light control using such a weakcontrol light intensity which is sufficiently practical. One of the mostimportant points for manufacturing the optical electronics element ishow a large nonlinear optical effect can be caused by a weak controllight intensity. This gives a solution whether the actual opticalelectronics element can be manufactured or not.

Therefore, in order to attain the actual light-light control, materialor structure having a large nonlinear optical effect must be obtained bysome methods. In order to obtain these materials or the structure, thenonlinear susceptibility is enhanced by artificially producing lowdimensional material or very fine structures, in which electrons arequantum-mechanically confined and the oscillator strength isconcentrated on a lowest excitation level. This is a major interest forthe quantum confinement effect of the electronic system.

But, in the material such as semiconductors having large interactionbetween atoms, a relation between the susceptibility and the actualresponse output is not so simple. Therefore, the amount of the nonlinearoptical effect cannot be fully evaluated by only evaluating thesusceptibility of the material. The above limitation has not been wellrecognized so far, and also the theoretical method of evaluating thenonlinear optical susceptibility has not been correctly and wellunderstood. Therefore, there is no established principle for producingmaterial or structural bodies having a large nonlinear optical effect.Accordingly, no practical material and no structural body having such anonlinear optical body have been realized so far.

It is, therefore, a primary object of the present invention to provide anonlinear optical element in which a sample size is selected so that theoptical electric field, that is, the exciton polariton electric field,resonated with excitons, becomes maximum.

It is another object of the present invention to provide a nonlinearoptical element having an enhanced nonlinear optical effect whichoperates with a remarkably weak input light or input control light.

It is another object of the present invention to provide a nonlinearoptical element for use in an light-light switching element or a opticalmemory element of a light information system which is controlled by acontrol light.

SUMMARY OF THE INVENTION

According to one aspect of the present invention, a nonlinear opticalelement includes an optical active layer comprised of dielectric samplesor semiconductor samples which cause a nonlinear optical effect, whereintheir shapes and sizes are selected so that an electric field of excitonresonance energy in the above sample is enhanced in resonance with thesize of the above sample to enhance the nonlinear optical effect.

According to another aspect of the present invention, a nonlinearoptical element includes a plurality of optical active layers and aplurality of barrier layers, each optical active layer having dielectricsamples or semiconductor samples which cause a nonlinear optical effect,wherein their shapes and sizes are selected so that the electric fieldof exciton resonance energy in the above sample increases in resonancewith the size of the above sample to enhance the nonlinear opticaleffect.

According to another aspect of the present invention, a nonlinearoptical element includes an optical active layer having dielectricsamples or semiconductor samples, wherein a size of said optical activelayer is selected to a size within the region whose center coincideswith the size at which an internal electric field as a function of thesize takes a peak value, and whose width is 2 times that of a full widthat half maximum of this peak.

According to another aspect of the present invention, a nonlinearoptical element includes a plurality of optical active layers and aplurality of barrier layers, wherein shapes and sizes of one or twodirections of said optical active layer are selected toquantum-mechanically confine the relative motion of excitons so that theoscillator strength and binding energy of excitons in material becomelarger than those of excitons in natural material.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a conceptual figure showing an operation of a nonlinearoptical element of a first embodiment of the present invention.

FIG. 2 shows a function of an amount of imaginary part of thethird-order nonlinear susceptibility corresponding to the amount of thesample size and the amount of the transfer energy in the model.

FIG. 3 shows characteristics of polariton energy dispersion where thereis no energy transfer in the material.

FIG. 4 shows characteristics of reflection factor spectrum distributionnear the exciton resonance area where there is no energy transfer in thematerial.

FIG. 5 shows an internal electric field which is a function of filmthickness when assuming the transfer energy of CuCl is 0.

FIG. 6 shows energy dispersion of polariton in relation to light andexciton when the energy transfer is finite.

FIG. 7 shows characteristics of internal electric field intensityagainst the film thickness in CuCl thin film.

FIG. 8 shows characteristics of nonlinear dielectric constant which iscalculated by multiplying internal electric field by nonlinearsusceptibility against the film thickness.

FIG.9 is a conceptual diagram showing a nonlinear optical element of asecond embodiment of the present invention.

FIG.10 is a conceptual diagram showing a nonlinear optical element of athird embodiment of the present invention.

FIG. 11 is a conceptual diagram showing a nonlinear optical element of afourth embodiment of the present invention.

FIG. 12 is a conceptual diagram showing a nonlinear optical element of afifth embodiment of the present invention.

FIG. 13 is a conceptual diagram showing a nonlinear optical element of asixth embodiment of the present invention.

FIG. 14 is a conceptual diagram showing a conventional nonlinear opticalelement.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 is a conceptual figure showing an operation of a nonlinearoptical element of a first embodiment of the present invention. In FIG.1, 1 is a film comprised of CuCl which is nonlinear optical material, 4is an input light, and 5 is a control light. 6 is an output light causedby the input light 4 which passes through the CuCl film 1. 7 is areflection light which is a portion of the input light 4 reflected atthe surface of the CuCl film 1. In the figure, d shows thickness of thefilm 1, that is, sample size.

A general explanation follows about the non-linear optical effect. Theamount of the non-linear optical effect is defined by the amount of thenonlinear susceptibility referred to as nonlinear response function andelectric field intensity in the material. As described above, the amountof the nonlinear optical effect is closely related with the amount ofthe nonlinear polarization.

In general, a component of the angular frequency ω of the polarization Pat a site j which is induced by the electrical field of the lightinputted into the material, is written by the expansion of the powerseries of the internal electrical field as shown in a below equation(1). ##EQU1## where, ω_(p), ω_(q), ω_(s) are angular frequencies of theinput light, j, l, m, n are indices of the lattice site. For simplifyingthe explanation, the deviation light is fixed by one plane. χ is aresponse coefficient for the input light which is determined only by thematerial property, for example CuCl in this case, and referred to asoptical response function or optical susceptibility. On the other hand,F shows electric field of exciton polariton in the media, namelyinternal electric field, which is a coupled wave of input light in themedia and induced polarization wave.

When the input light intensity is small, the higher order term of theinternal electric field can be neglected and the induced polarization isproportional to the first order of the internal electric field. This isreferred to as a linear response. But, when the input light intensitybecomes larger, a component proportional to the higher order of theinternal optical electric field can no longer be neglected, and then theoutput light intensity is not proportional to the input light intensitydue to the influence of the nonlinear effect. The second and subsequentterms in the equation (1) show components of the nonlinear polarization.The second term shows nonlinearity which is strongly present in thematerial having no inversion symmetry. In case of normal isotropicmaterial, the third term becomes the largest nonlinear term.

In the material in which the interaction can not be neglected betweenatoms, the optical susceptibility χ and the internal electric field aregenerally functions of the coordinate, and its amount is defined at eachcoordinate site. Especially, the susceptibility is defined by aplurality of coordinates. This means that an induced polarization at onepoint is affected by the internal optical electric field from all otherpoints. Such a response is referred to as a non-local response. Forexample, the third-order nonlinear susceptibility is a function of fourcoordinates and the third-order nonlinear polarization at the site j isaffected by the plural modes of electric field at all sites of thecrystal. The effect of the non-local response plays an essential rollfor enhancement the effect of the internal electric field.

In case of isolated atoms or molecules, or material constructed ofnon-interacting atoms or molecules, the amount of nonlinear opticaleffect per unit volume does not depend on a size or a shape of thesample. But, in case of the system in which collected atoms are notisolated from each other but have a relation via the electronicinteraction, such as semiconductor or dielectric media like CuCl in thisembodiment, the amount of nonlinear optical effect is affected byvarious sizes or shapes of the sample due to the following two reasons.

The first reason is that the amount of the nonlinear opticalsusceptibility of such system depends upon a size of the sample. Thesecond reason is that the amount of the internal electric field ofexciton polariton is peculiarly enhanced in resonance with the samplesize according to the interference effect. If the size and the shape ofthe sample are controlled so that the above two effects are to be usedeffectively, a large nonlinear optical effect can be obtained whichcould not be obtained in the past.

The following is a detailed explanation of sample-size dependence of anamount of the nonlinear optical response function and the internalelectric field using the example of the third-order nonlinear opticaleffect. The former is explained in the paper by H. Ishihara and K. Cho,Physical Review B Vol. 42, p 1724 (1990), and H. Ishihara and K. Cho,International Journal of Nonlinear Optical Physics (World Scientific),Vol. 1, p 287 (1992).

At first, the sample size dependence of the third nonlinear opticalsusceptibility is explained here. This dependence is decided for acertain input light energy by the amount of jumping probability of theexcitation between the atoms (amount of the transfer energy) which areproper to the material, and by the length of the life time of theexcitation state of the crystal. In the optical effect of the excitonicsystem, the polarization is carried by the excitons, where the excitonis a complex particle in which excited electrons and remaining holes arebound each other by the Coulomb force and a quantum state which existsas a lowest excitation state of the crystal. There are two kinds ofexcitons, one of them is a Frenkel exciton, where excited electrons andholes exist on the same atom, having no internal degree of freedom.Another is a Wannier exciton where excited electrons and holes can existon different atoms. The Frenkel exciton is used in order to simplify theexplanation when the concrete expression of exciton is necessary. But aresult is obtained as a general form which can be applied to the casewhere the exciton has a degree of freedom of the relative motion.

The third-order nonlinear optical process of the exciton systemgenerally consists of the following two processes.

(1) produce one-exciton→annihilate it and return to the groundstate→produce another exciton→annihilate another exciton and return tothe ground state again.

(2) produce one-exciton→produce another exciton to provide a statehaving two-excitons→annihilate one-exciton and return to one-excitonstate→annihilate another exciton and return to the ground state.

The former process is referred to as A₀ process and the latter processis referred to as A₂ process. The linear response only relates to aprocess in which one-exciton is produced and then annihilated.

Two kinds of sixteen terms in total, which show the above two processes,are obtained by the calculating the third-order nonlinear susceptibilityusing the perturbation expansion method of the density matrix which iswell established in the quantum mechanics. In the process A₀, an amountof response is proportional to the fourth power of transition dipolemoment between the ground state and the exciton state. This is clearlyunderstood by concretely expressing one of the terms showing the processusing the perturbation expansion of the density matrix.

For example, one of the terms of A₀ is proportional to the followingexpression (2). ##EQU2##

The summation of λ, μ shows that this term includes a sum of manyprocesses relating various quantum states, where, |λ> is one-excitonstate having quantum number λ, |0> is ground state, P is a dipoleoperator of the crystal, E.sub.λ is an eigenenergy of state |λ>, andω_(p), ω_(q), ω_(s) are angular frequencies of the input lights. γ is afactor of adiabatic switching of the interaction between electrons andlights. A value which the Plank constant is divided by 2π, is taken tobe unity, and hereafter it is followed. <O|P|λ> in the numerator is amatrix element of the transition dipole moment. The square of theabsolute value of <0|P|λ> depends on the space volume occupied by theexciton wave function of the state |λ>. Since the exciton wave functionin a system having energy transfer is spread in whole crystal, the aboveamount increases in proportion to the increase in volume.

A more detailed explanation is given below. For example, the Frenkelexciton confined in the thin film having a z axis is expressed byequation (3) using the excitation state |l_(x) l_(y) n) localized at thelattice site (l_(x), l_(y), n) ##EQU3## then, the expression of<0|P|K_(x) K_(y) k> is obtained as ##EQU4## where, |K_(x) K_(y) k> is aFrenkel exciton state having a wave number (K_(x), K_(y)) which isparallel to the surface of thin film and a wave number k which isperpendicular to the surface. N_(x), l_(x) are the number of atoms andan index of the atom site in the line along x direction on the surface,respectively. N_(y), l_(y) are the number of atoms and an index of theatom site in the line along y direction on the surface, respectively.N_(z), n are the number of atoms and an index of the atom site alongz-axis, respectively. The 4th power of the value calculated above is inproportion to the square of the sample volume. Therefore, the A₀ perunit volume has an amount in proportion to the volume of the sample. Onthe other hand, the contributions of the process of A₂ have the oppositesign to the process of A₀.

In the system having no energy transfer and no dispersion of excitedenergy, the exciton wave function is localized on the atom and anyexciton on every atom has the same resonance energy. If doubleexcitations on the same atom is allowed, the contribution of the processA₀ and A₂ is completely canceled. But, since double excitations cannotactually exist by the Pauli exclusion principle, there arises adifference of the degrees of freedom between the two kinds of processes,and cancellation becomes incomplete. As a result, an amount ofcontribution is the same as that of the isolated atom multiplied by adensity of atom, and has no dependence on the sample size.

But, in the system having finite transfer energy, the exciton stateforms a band and causes the energy to disperse on the band. And sincethe energy of the state having two-excitons is also dispersed on theband in the same way, the energy differences between lowest one-excitonstate and two-excitons states shift from that between ground state andlowest one-exciton state. When the band width is large, and the samplesize is so small that the number of exciton states is small, and theamount of above mentioned shift is large. In this case, the cancellationhardly occurs. As long as the state is maintained, the contribution ofeach process increases along with the volume at a separate energy site,and the amount of the nonlinear optical effect per unit volume isproportional to the sample size.

But, when sample size becomes large and a state having two-excitons isfilled densely in a certain bandwidth, the drift of the resonance sitebetween the two kinds of processes becomes small and cancellation occursbetween these processes. It depends on the width of each resonance peakand to what extent the cancellation occurs. That is, the overlapped partof the energy and the extent of the cancellation become greater as thepeak width becomes larger. Since the width of the resonance peak isinversely proportional to the life time of the excitation state, thecancellation becomes harder to achieve as the life time is longer. Ifthe sample size becomes still larger, the enhancement of whole nonlinearsusceptibility by its volume is saturated and becomes a constant valueafter the value reaches a maximum value. To know what extent is thenonlinear susceptibility continuously enhanced with the increase of thesample size is very important for estimating the amount of the nonlinearoptical effect. This is, as easily seen from the above description,determined by the parameters corresponding to the material such as theamount of transfer energy which defines the band width and the lifetimeof the excitation which defines a width of the resonance peak.

The above is summarized as follows. That is, the whole value of thethird-order nonlinear susceptibility increases in proportion to thesample size when the sample size is small, then its value is saturatedby cancellation and becomes a constant value. If the above is reverselyexpressed, the larger the transfer energy is, the greater the samplesize region is where the nonlinear susceptibility increases according tothe increase of the sample size. Further, the longer the lifetime of theexcitation state is, the stronger the tendency is. Further, since thetransfer energy is inversely proportional to the effective mass of theexciton, the size dependence in relation to the parameter of effectivemass can be discussed in the similar way.

The detailed mechanism of the nonlinear optical effect described abovebecomes apparent from the theoretical calculation using the perturbationexpansion method of the density matrix of the quantum mechanics.

A detailed calculation is described in the following. From the result ofthe calculation by the density matrix method, the third-order nonlinearpolarization on the lattice site j, is written as, ##EQU5## where, F_(n)(ω_(s)) is the amplitude of the light electric field having frequencyω_(s) on the lattice site n. For simplifying the explanation, the lightpolarization is fixed to a certain direction.

ω.sup.(3) j 1 mn (ω_(p),ω_(q),ω_(s))is a site represented third-ordernonlinear susceptibility, and the details are obtained from thefollowing expression (6). ##EQU6## where, v₀ is a volume of unit a cell,P_(j) is a polarization density operator at lattice site j. E.sub.ξ isan eigenenergy at the state |ξ> where there is no external field, andobtained from following equations.

    E.sub.ξη =E.sub.ξ -E.sub.η                   (7)

    Ω'.sub.3 =ω.sub.p +ω.sub.q +ω.sub.s +3i.sub.γ(8)

    Ω'.sub.2 =ω.sub.q +ω.sub.s +2i.sub.γ(9)

    ω'.sub.s =ω.sub.s +i.sub.γ               (10)

|λ>, |ν> in the expression (6) take the place of one-exciton state, and|μ> takes the place of a state having two-excitons or a ground state. Bysubstituting the eigenfunction and eigenenergy of this one-exciton stateand the state having two-excitons into the above expression according tothe handling system, the concrete expression of the nonlinearsusceptibility is obtained.

The nonlinear susceptibility which is calculated in this way is afunction of four coordinates. In usual case, this is evaluated with useof so-called long wavelength approximation, where the site dependence ofthe electric field is omitted. As a result of this approximation, thesite dependence of nonlinear susceptibility is removed. Though thisapproximation is used in the following explanation, the conclusion isquite general. Under the long wavelength approximation, the third-ordernonlinear polarization is expressed as, ##EQU7## where, the sitedependence of the nonlinear susceptibility disappears.

In the following simplest example, the exciton state is calculated inthe model having one-dimensional energy transfer. Then the amount of thethird-order nonlinear susceptibility is concretely calculated when theincident light beam resonates with the energy of lowest one-excitonstate.

In the following example, a pump-probe measurement, in which theintensity of the weak probe light (signal light) is controlled by thestrong pumping light (control light), is considered. That is, thepumping light frequency and the probe light frequency are substitutedinto the frequencies ω_(p), ω_(q), ω_(s) of the electric field. Theeigenfunction and eigenenergy of the one-exciton state and the statehaving two-excitons are calculated in case of the Frenkel excitons onthe one-dimensional periodic lattice. The above is the simplest example.But, the present discussion on the sample-size dependence of thethird-order nonlinear susceptibility, that is, the enhancement andsucceeding saturation of χ.sup.(3) with increase of the sample size doesnot depend on the model. If it is necessary to obtain a quantitative andaccurate result in an actual system, the exciton state of the handlingsystem can be calculated analytically or numerically.

In the Frenkel exciton system on the one-dimensional periodic lattice,the eigenenergy and the eigenfunction are obtained as, ##EQU8##respectively, where, εo shows energy when the excitation is localized onthe lattice site,

b shows transfer energy, N is the number of lattice, and |l) shows anexcitation state which is localized on the lattice site l. The allowedvalues of the wave number k are

    K=2nπ/N, {n=1,2 . . . ,N}.                              (14)

On the other hand, in case of considering the Pauli exclusion principlein which double excitations on the same site cannot actually be allowed,a state having two-excitons is specified by the two quantum numberscorresponding to the wave number of the center-of-mass motion and wavenumber of relative motion.

The eigenenergy and the eigenfunction are obtained as, ##EQU9##respectively, where, |l, m) shows a state where the excitation exists atl, m sites. The allowed values of wave number K, κ are determined asfollows. When N is an odd number:

    (K,κ)={2m,(2n-1)}π/N, {m=1,2, . . . , N, n=1,2, . . . , (N-1)/2}(17)

When N is an even number: ##EQU10##

FIG. 2 shows an imaginary part of the third-order nonlinearsusceptibility as a function of the sample size N and transfer energy bin the above model. In this case, both the pumping light and the probelight are tuned with lowest one-exciton resonance energy, and also theinternal electric field is approximated as having no dependence on site(long wavelength approximation). It is easily understood from FIG. 2,the third-order nonlinear susceptibility becomes larger, at the site offixed transfer energy, in proportion to the sample size within thelimited sample size area then the amount becomes a constant value afterreaching a maximum peak value.

The sample size area where χ.sup.(3) shows enhancement is determined bythe amount of the transfer energy and the lifetime of the excitationstate. That is, the greater the transfer energy becomes and the longerthe lifetime becomes, the larger the area where the third-ordersusceptibility is enhanced in proportion to the sample size becomes. Inthe above calculation, the lifetime is introduced by treating a factor γof the adiabatic switching used for interaction between the electron andthe light as a finite value.

In case of CuCl of the present embodiment, the transfer energy and thetypical relaxation constant (inverse number of the lifetime) areestimated as 57 meV, 0.06 meV, respectively, from the parameters knownby the experiment. By substituting these values in the aboveexpressions, the third-order nonlinear susceptibility (per unit volume)of the present model is about 60 times at the maximum site compared withthe case of one atom. This occurs when the number of atomic layers N=82.

Next, the singular enhancement effect of the internal electric fieldintensity is explained using the size resonance enhancement effect ofthe exciton polariton in the thin film structure in FIG. 1 as anexample.

In general, when the light having energy resonated within the excitoninputs into the material, a coupled wave is generated by the externalfield inputted into the material and the polarization wave generated bythe exciton. This is referred to as an exciton polariton. The internalelectric field of the system is generated by this exciton polariton.

FIG. 3 shows characteristics of a polariton energy dispersion wherethere is no energy transfer in the material.

FIG. 4 shows characteristics of a reflection spectrum near the excitonresonance region where there is no energy transfer in the material.

In FIG. 3, A is a dispersion curve of light, B is a dispersion curve ofthe exciton, C is a dispersion curve of the polariton (lower branch),and D is a dispersion curve of the polariton (upper branch). ω_(L) isthe energy of a longitudinal wave, and ω_(T) is the energy of atransversal wave.

As seen in FIG. 3 and FIG. 4, where no energy transfer exists, there isgenerally an energy area where there is no light mode over the resonanceenergy ω_(T). At this area, the light cannot enter into the crystalmaterial and the light totally reflects at its surface. When thereexists a relaxation mechanism of the excitation energy, a very smallamount of light can enter into the crystal material and its amplitude isvery small. In this case, internal electric field with the resonanceenergy becomes a certain amount of intensity when the sample is verythin such as a film including a few atomic layers. But, the filmthickness becomes thicker, and the intensity rapidly decreases to asmall value. For example, assuming that the thin film has a resonanceenergy of CuCl and is formed of material having zero transfer energy,the average internal electric field intensity over the layers is 0.0006in the case that the intensity of the incident light is unity and therelaxation constant is 0.06 meV, and the film thickness is 52 atomiclayers (about 280 Å).

FIG. 5 shows an average intensity of internal electric field over thelayers which is a function of film thickness assuming that the transferenergy of CuCl is 0.

In fact, there exists energy transfer in the material such as CuCl. Insuch a case, the dispersion relation of the polariton differs from theabove case, and the electromagnetic wave mode exists in the resonanceenergy area. This case is shown in FIG. 6.

FIG. 6 shows energy dispersion of polariton when the energy transfer isfinite. In the figure, notations are the same as those in FIG. 3 andFIG. 4.

The exciton polariton wave causes a similar interference effect as theFabry Perot type of interference effect in the thin film. As seen fromFIG. 6, in the resonance energy area, the wavelength of theelectromagnetic wave is very small compared with normal light, thus aspecial interference effect is caused. As a result of the interferenceeffect, the reflectance happens to be very small even for the inputlight with the resonance energy for some special sample thickness. Forthe above case, the exciton polariton resonates with sample size and itsamplitude is singularly enhanced.

FIG. 7 shows an film-thickness dependence of a internal electric fieldintensity obtained by calculation for the case of CuCl. In the figure,LT splitting is the value which is proportional to the transition dipolemoment per atom. The vertical axis shows the internal electric fieldintensity normalized by the input light intensity, and the horizontalaxis shows the size of the thin film, that is, the film thickness. Thefirst peak value is 0.248 in case of CuCl, which is 80 times largercompared with the value near 12 atomic layers where the resonantenhancement does not take place.

The above result is obtained from the following theoretical calculation.At first, the eigenenergy and eigenfunction in the absence of theexternal light are obtained by considering the energy transfer effect ofthe system by the quantum mechanics calculation. Then, using the aboveresult, a linear susceptibility is obtained as a function of twocoordinates from the following expression (19) by the linear responsetheory. ##EQU11## where, R is a coordinate which indicates a site of thecell, P(R) is a polarization density operator at a point R, and λ is aquantum number indicating an excitation state of the system havingexcitation energy E.sub.λ. |λ> shows its quantum state, and |0> showsground state.

For example, in case of Frenkel exciton confined in a thin film, a wavefunction is expressed by the equation (3), and the eigenenergy isexpressed by the equation (12) when the kinetic energy parallel to thethin film is to be 0. The susceptibility factor is expressed by thefunction of two coordinates, because the nonlocal response is consideredwhere the polarization at one site is induced not only by the electricfield on the same site, but also by that on other sites.

At last, the electric field in material is obtained by solving thefollowing Maxwell equation (20), containing this nonlocal susceptibilityas a integral kernel.

    rotrotF(R)-(ω.sup.2 /c.sup.2)F(R)-(4πω.sup.2 /c.sup.2)∫dR'ω.sup.(1) (R,R';ω)F(R')=0   (20)

In case of normal incident of light into the thin film consisting of thediscrete lattice and having N atomic layers, the electric field isconcretely calculated as, ##EQU12## where, {F_(j), F_(j) } are arbitraryconstants, and wave numbers {k_(j) } are the roots of the polaritondispersion relation shown in the following equation (22). ##EQU13## anda₀, ε_(b) are lattice constant and background dielectric constant,respectively, and M is the transition dipole moment per atom.

The additional boundary conditions, which define relations between anarbitrary constants {Fj, Fj} at the same time as solving the Maxwellequation, is obtained as, ##EQU14##

By connecting the internal light with an outside light using the aboveequations and Maxwell boundary condition, that is, the continuitycondition between electric field and magnetic field at the boundary, thevalue of the unfixed constants such as {Fj, Fj } can be determined, andthus the internal electric filed intensity is obtained.

In the past, there is no example in which an internal electric field ofthe excitonic system is calculated by using the similar method asdescribed above. The theory explained above is described in detail inthe references, K. Cho and M. Kawata; J. Phys. Soc. Japan, vol. 54(1985), p 4431, and K. Cho and H. Ishihara: J. Phys. Soc. Japan, vol. 59(1990), p 754.

Since the above calculated result is obtained by a linear opticalresponse theory, deviation of an internal electric field, which isgenerated by the nonlinear optical effect and exists at an actualnonlinear optical response, is not included in the above result. FIG. 7shows such a calculated result without considering the nonlinear opticaleffect. However, the deviation of the internal electric field intensityby the nonlinear optical effect is not so large that it givesqualitative changes to the above explanation. Accordingly, thisdeviation can be neglected.

As described above, by using the sample size dependence of thethird-order nonlinear susceptibility and the size resonance enhancementeffect of the internal electric field, the nonlinear optical effect ofthe medium can be drawn maximally. That is, as described above, in thematerial having large transfer energy, the third-order nonlinear opticalsusceptibility becomes larger in comparison with the material havingzero transfer energy when its sample size becomes larger. For example,in case of CuCl, the value reaches up to 60 times. But, if in the casethat the size resonance enhancement of internal field does not occur,the enhancement of nonlinear susceptibility is not made the best use of.For example, if CuCl thin film having thickness of 20 atomic layers(about 108 Å) is selected, since the internal electric field is notenhanced as seen from FIG. 7, the size enhancement effect of thenonlinear optical susceptibility is not used effectively, and a largenonlinear optical effect can not be obtained.

In case of obtaining large nonlinear optical effect by enhancing theoscillator strength by confining the electronic system, sometimes smallsample size is apt to be selected. But, as is easily understood from theabove description, while the sample size becomes small, the remarkablenonlinear optical effect cannot be obtained unless the sample size isselected so that the size resonance enhancement of the internal fieldoccurs. If a larger sample size is selected, for example, film thicknesshaving 1000 atomic layers (about 5400 Å) of CuCl thin film, theremarkable nonlinear optical effect cannot be obtained since theinternal electric field intensity is very small as seen in FIG. 7.

But, if a film thickness having 52 atomic layers (about 280 Å) isselected as shown in FIG. 7, a very large nonlinear optical effect canbe obtained compared with the case of having no resonance enhancementsince the size resonance enhancement of the internal electric fieldoccurs. If the sample size is in accordance with the area where thevalue of the nonlinear susceptibility becomes maximum, the nonlinearpart of signal intensity of the output light will increase more than 2˜3digits compared with the case When resonance enhancement of the internalelectric field does not occur at micro size.

FIG. 8 shows characteristics of a nonlinear dielectric constant as afunction of the film thickness which is calculated by multiplying theinternal electric field average over the layers by nonlinearsusceptibility, in which the site dependence is neglected. As understoodfrom the figure, the nonlinear dielectric constant singularly increasesat the site where the internal electric field is enhanced resonantlywith size.

Therefore, if the sample size area, where the internal electric fieldsingularly enhances, is selected, it is able to obtain a nonlinearoptical structure, which has a very large nonlinear optical effect, andcan be operated by a weak control light, and be actually used in theoptoelectronics field.

In this embodiment, an example of the nonlinear optical structure usingCuCl is shown. But, as will be appreciated by those skilled in the art,other material such as CuBr, CdS, CdSe, ZnSe, GaAs and InP can be alsoused.

Until now, the nonlinear optical effect as described above has not beenavailable. There are mainly three reasons as described below.

The sample size area where the large nonlinear optical effect occurs byconfining an electronic system is considered to exist at a very smallsample size area compared with the area where the size resonanceenhancement of the internal electric field actually occurs. Therefore,nobody has paid any attention to the sample size area described abovewhich is important for the nonlinear optical effect.

Only size dependence of the nonlinear susceptibility has been consideredbut the size dependence of the internal electric field has not beenconsidered.

Further, with respect to the sample size area as described above, whichis important for the nonlinear optical effect, it is considered thatthere is no enhancement effect of the nonlinear susceptibility by thequantum effect, and a large nonlinear optical effect can not beexpected.

In the above explanation, the size resonance enhancement effect of theinternal electric field in a thin film shape is described. But, thiseffect is not restricted by the sample shape. Since this effect occursby controlling a size of a certain dimension of the sample, a wireshape, box shape, sphere shape other than the thin film described abovecan be used for obtaining this effect. That is, a very large nonlinearoptical effect can be obtained by controlling the width or radius of thequantum wires, quantum boxes or fine particles etc.

FIG. 9 is a conceptual diagram showing a nonlinear optical element of asecond embodiment of the present invention. In this figure, 12 areactive layers. The thickness d of an active layer 12 is selected so thatthe size resonance enhancement of the internal electric field intensityis generated. 22 are barrier layers. 3 is a substrate. Other numeralsare the same as those in FIG. 1.

An optically active layer 12 made of CuCl or ZnSe and a barrier layer 22are laminated alternatively by epitaxial growth on the substrate 3 andform a super lattice structure. The band gap and thickness of thebarrier layer 22 are selected so that electronic state of each opticalactive layer 12 are separated. The thickness of all optical activelayers 12 are selected to be d where the intensity of the electric fieldof controlling light having exciton resonance energy is enhancedresonantly with size. When the nonlinear optical effect occurs when thetransmitted light 6 is used, the substrate 3 must be removed by, forexample, an etching method. But, when the nonlinear optical effect whichappears in the reflection light 7 is used, the substrate 3 does not needto be removed. As described above, the nonlinear optical effectincreases by laminating a plurality of nonlinear optical materialalternatively.

FIG. 10 is a conceptual diagram showing a nonlinear optical element of athird embodiment of the present invention. In the figure, 13 is aparticulate comprised of material showing the nonlinear optical effect.The radius of the particulate 13 is controlled so that the internalelectric field intensity is enhanced resonately with size. 23 is adielectric such as glass, in which the particulates 13 are doped. Otherreference numerals for like elements are the same as those in FIG. 1.Many kind of shapes of a nonlinear optical element can be obtained usingthe above structure.

FIG. 11 is a conceptual diagram showing a nonlinear optical element of afourth embodiment of the present invention. In the figure, 14 is aquantum wire, comprised of material such as semiconductor showing thenonlinear optical effect. The sample size of the quantum wire 14 iscontrolled so that the internal electric field intensity is enhancedresonately with size. 24 is a barrier portion. Other reference numeralsfor like elements are the same as those in FIG. 1. The quantum wire 14and barrier portions 24 are produced by selective growth of epitaxiallayers or by etching.

FIG. 12 is a conceptual diagram showing a nonlinear optical element of afifth embodiment of the present invention. In the figure, 15 is aquantum box, comprised of material such as semiconductor showing thenonlinear optical effect. The sample size of the quantum box 15 iscontrolled so that the internal electric field intensity is enhancedresonately with size. 25 is a barrier portion. Other reference numeralsfor like elements are the same as those in FIG. 1. The quantum boxes 15and barrier portions 25 are produced by selective growth of epitaxiallayers or by etching.

FIG. 13 is a conceptual diagram showing a nonlinear optical element of asixth embodiment of the present invention. In the figure, 16 is aquantum board, comprised of material such as semiconductor showing thenonlinear optical effect. Depth d of the quantum board 16 is controlledso that the relative motion of the Wannier exciton is confined to maketwo dimensional excitons, and width w is controlled so thatcenter-of-mass motion of the exciton is confined to drive the sizeresonance enhancement of the internal electric field intensity. 26 is abarrier portion. Other reference numerals for like elements are the sameas those in FIG. 1. The quantum board 16 and barrier portion 26 areproduced by selective growth of epitaxial layers or by etching. By thisstructure, a large nonlinear optical effect can be obtained at the roomtemperature.

The peak value of the internal electric field intensity shown in FIG. 7is sharper if the LT splitting of the material is larger. That is,although the internal electric field usually considerably attenuates inthe material having large LT splitting, it is remarkably enhanced if theinternal electric field resonates with the sample size. Until now, inorder to obtain material having a large nonlinear optical effect,material having a large transition dipole moment per atom (M) has beensought. Further, greater effort has been made for enlarging thetransition dipole moment M by processing the material into a twodimensional excitonic system. Since, the transition dipole moment M isin proportion to the LT splitting, the material having a largetransition dipole moment M has also large LT splitting.

Therefore, in a case of using these materials, this invention has agreat advantage because there occurs a large difference according towhether or not one uses the enhancement effect of the internal electricfield. In case of the two dimensional excitonic system which confinesrelative motion of the exciton, the internal electric field is enhancedby confining the center-of-mass motion of the exciton in the remainingdegree of freedom.

In the above embodiment, a switch or modulation function which controlsthe transmission and reflection of signal light by control light isdescribed. These nonlinear optical effects can be applied to other manynonlinear optical elements, such as a four-wave mixing element oroptical bistable element.

In the above embodiment, nonlinear optical elements are explained, butthey can be also realized by a nonlinear optical structure having thesame effect.

Those skilled in the art will recognize that many modifications to theforegoing description can be made without departing from the spirit ofthe invention. The foregoing description is intended to be exemplary andin no way limiting. The scope of the invention is defined in theappended claims and equivalents thereto.

What is claimed is:
 1. A nonlinear optical element for receiving aninput light and a control light and producing an output lightcomprising:a plurality of quantum members of a predetermined shape whichcause a nonlinear optical effect on the output light; and a plurality ofbarrier portions, each barrier portion separating a quantum member fromanother quantum member; wherein the size of each quantum member isselected to be within a specific range such that an internal electricfield is maximized, the specific range having a center pointapproximately equal to a twice when the electric field is at a peakvalue and the specific range having a width being approximately equal totwice that of the width of a size range when the internal electric fieldis equal to or greater than half of the peak value.
 2. A nonlinearoptical element of claim 1 wherein said quantum members are comprised ofdielectric samples.
 3. A nonlinear optical element of claim 1 whereinsaid quantum members are comprised of semiconductor samples,
 4. Anonlinear optical element of claim 1 wherein said quantum members arecomprised of CuCl.
 5. A nonlinear optical element of claim 1 whereinsaid quantum members are comprised of ZnSe.
 6. A nonlinear opticalelement of claim 1 wherein each of the quantum, members is comprised ofa thin film shape sample.
 7. A nonlinear optical element of claim 1wherein each of the quantum members is comprised of a sphere shapesample.
 8. A nonlinear optical element of claim 1 wherein each of saidquantum members is comprised of a bar shape sample.
 9. A nonlinearoptical element of claim 1 wherein each of the quantum members iscomprised of a box shape sample.
 10. A nonlinear optical elementcomprising:a barrier portion; a plurality of quantum members embedded inthe barrier portion and receiving an input light and a control light andproducing an output light having a nonlinear optical effect, wherein theelement includes an internal electric field which varies as a functionof the size of each quantum member, each quantum member is selected tobe within a predetermined size range having a center point approximatelyequal to a size at which the internal electric field is substantially ata pear value, and the range having a width being 2 times that of ahalf-peak width, the half-peak width being equal to a size range whenthe electric field is equal to or greater than half of peak value.
 11. Anonlinear optical element comprising:a barrier portion; a plurality ofquantum members embedded in the barrier potion and receiving an inputlight and a control light and producing an output light having anonlinear optical effect, wherein the element has an internal electricfield which varies as a function of the size of each quantum member, andwherein the shape of each of the quantum members is such that there aretwo sizes in two different directions, a first size in a first directionis selected to maximize the internal electric field and a second size ina second direction is selected to quantum-mechanically confine therelative motion of excitons so that oscillator strength and bindingenergy of excitons in quantum material become larger than those ofexcitons in non-quantum natural material.
 12. A nonlinear opticalelement comprising:a barrier member; and a plurality of optical activemembers dispersed substantially evenly within the barrier member;wherein the optical active members cause a nonlinear optical effect, andeach optical active member has a predetermined size so that an electricfield of exciton resonance energy, which varies as function of the sizeof the optical active members, in the element is maximized, the size ofeach optical active member being within a range having a width which istwice that of the width of a size range when the internal electric fieldis at least as great as half of its peak value.
 13. A nonlinear opticalelement of claim 12 wherein said optical active members are comprised ofdielectric samples.
 14. A nonlinear optical element of claim 12 whereinsaid optical active members are comprised of semiconductor samples. 15.A nonlinear optical element of claim 12 wherein said optical activemembers are comprised of CuCl.
 16. A nonlinear optical element of claim12 wherein said optical active members are comprised of ZnSe.
 17. Anonlinear optical element of claim 12 wherein each of said opticalactive members is comprised of a thin film shape sample.
 18. A nonlinearoptical element of claim 12 wherein each of said optical active membersis comprised of a sphere shape sample.
 19. A nonlinear optical elementof claim 12 wherein each of said optical active members is comprised ofa bar shape sample.
 20. A nonlinear optical element of claim 12 whereineach of said optical active members is comprised of a box shape sample.21. A nonlinear optical element comprising:a barrier portion; at leastone Optical active member embedded within the barrier portion; andwherein the optical active member causes a nonlinear optical effect,wherein an internal electric field varies as a function of the size ofthe quantum member, the quantum member is selected to be within apredetermined size range having a center point approximately equal to asize at which the internal electric field is substantially at a peakvalue, and the range having a width being 2 times that of a width of asize range of the quantum member when the electric field is equal to orgreater than half of the peak value.
 22. A nonlinear optical elementcomprising:a barrier portion; a plurality of optical active membersdispersed substantially evenly within the substrate; and wherein theoptical active members cause a nonlinear optical effect, and wherein theshape of each of the quantum members is such that there are two sizes intwo different directions, a first size in a first direction is selectedto maximize the internal electric field and a second size in a seconddirection is selected to quantum-mechanically confine the relativemotion of excitons so that oscillator strength and binding energy ofexcitons in quantum material become larger than those of excitons innon-quantum natural material.
 23. A method for producing a non-linearoptical element comprising the steps of:providing a barrier portion;embedding a plurality of optical active members substantially evenlywithin the barrier portion; wherein each barrier portion separates anoptical active member from another optical active member; and selectinga size of each optical active member to be within a range having a widthwhich is twice the width of a size range of an optical active memberwhen an internal electric field is at least as great as half of its peakvalue.
 24. A method as claimed in claim 23 wherein the step of selectingincludes the step of selecting the shape of each optical active membersuch that each optical active member is in the shape of a bar.
 25. Amethod as claimed in claim 23 wherein the step of selecting includes thestep of selecting the shape of each optical active member such that eachoptical active member is in the shape of a box.